Knozen, a free iPhone app, allows colleagues to rate each other on traits such as assertiveness, patience, analytical ability, friendliness and skepticism.
"Knowing more about yourself is a gift, and knowing more about how you're perceiving others and where it's different and where it's the same can be really useful," said Marc Cenedella, the founder and chief executive officer of New York-based Knozen.
The app, which operates via a work email address when at least seven colleagues in the same company are signed up, poses questions about which colleague is likely to exhibit a particular personality trait such as assertiveness or patience.
All the questions are positive, according to Cenedella, and aimed at assessing an employee's personality.
"The important thing is there are no bad traits. Someone can be structured and organized, or they might be unstructured and open to new things. Both are good, and there's no wrong answer in personality assessment," he said.
The app plots each person's results on a matrix showing personality traits on a scale of one to five. Users can also see the traits they are more prone to than others.
"When we say someone is patient it means that compared to everyone else they will be more likely to wait longer and not get snappy," Cenedella explained.
He added that greater self-awareness can help people work better in teams by understanding their strengths and weaknesses better.
Another free app for iPhone, Good.Co, which is available worldwide, lets people take quizzes to assess their personality and to receive feedback from contacts in their Facebook and LinkedIn networks.
"Many times feedback we receive from others is more honest than what we'd say about ourselves," said Samar Birwadker, chief executive officer of Good.Co, which is based in San Francisco.
The app uses positive questions and provides a score that measures the compatibility of employees with each other and with companies based on personality traits, attitudes and motivations.
"For individuals, self-awareness and self-discovery can help strengthen their career, but also improve other facets of their life as well, including interpersonal relationships," Birwadker said.
Ryan Ackers, a recruitment adviser at the Dutch human resources consulting firm Randstad, said self-awareness on the job is crucial for career success, happiness and compatibility with co-workers. But he said some employees could perceive the feedback negatively.
"When a person is asked to share their opinion on another person, a popularity contest can result, and though many may get lots out of the apps, some may be offended and even hurt," he said. "If they see themselves not getting rated the way they expect, it could create animosity and low morale."